The attack on the Cougar helicopter came as more than a dozen buses and trucks were torched in Guadalajara, Mexico's second biggest city, and a gang clashed with police in the town of Autlan.
Five banks were set on fire in the town of Ciudad Guzman, authorities said.
Authorities have not said who was responsible for the violence, but it came amid an escalation of violence by the Jalisco New Generation Drug Cartel, which killed 20 police officers in two ambushes in March and April.
"(The gunmen) attacked the military personnel with shots from firearms, hitting the Cougar helicopter, which conducted an emergency landing," the defense ministry said in a statement.
The helicopter was carrying 11 troops, five crew members and two federal police officers. They had spotted the gunmen on a road between the towns of Casimiro Castillo and Villa Purificacion when they were hit.
The two police officers and 10 soldiers were injured. They were taken to the military hospital of Guadalajara.
The location of the attack was near the town of Autlan, where a clash was reported between a gang and the authorities.
At least one police officer was killed and "an undetermined number" of gang members died in a shootout in Autlan, Jalisco state government spokesman Gonzalo Sanchez told Milenio television.
Starting at around 9:45 am in Guadalajara, buses and trucks were torched in at least a dozen streets, but Sanchez said no shootouts were reported in the western city.
Authorities did not say who set them on fire or why, but such tactics were used by the Gulf cartel in northern Tamaulipas state following major arrests last month.
"Remain calm. If you have any reason to leave your house, don't go out," the Jalisco state prosecutor's office said on Twitter.
Authorities said they had begun to douse the burning vehicles in Guadalajara. Vehicles were torched in other parts of the state.
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